Anyone knows the answer to this question? (1 Viewer)

[kaz1]

im in year 10 and i cant a figure out this question i got in maths:

A right angled triangle has a hypotenuse that is 3cm longer than the shortest side. What is the length of the hypotenuse?

and the perimeter of the triangle is 10cm

 

[Gavvvvvin]

You cant work it out.

 

[kaz1]

nope

 

[sanjeevprasad99]

…u can use algebraic expressions to get the answer….but u wont get a actual number, u will have x’s and stuff in it…..
U got the answer with u?

 

[sabira001]

Well if you want to work out the hypotenuse from the 2nd longest side (call it y), you have hypotenuse = (y^2 + 9)/6
Or... if you want it from the shortest side (call it z)... its z+3

I.e. there are an infinite number of solutions. But if you want all three numbers to be integers, that's a different story. But I don't know if there are any Pythagorean Triads like that.

 

[ellen.louise]

looking through a massive list of pythagorean triads, i couldn't find any that fit that. (yes, i know, i have no life ) but i might have missed one

what ya mean? there are plenty of solutions to that (try surds, mate)
the problem is, you would need to be given a length or an angle. Any at all. You could actually work it from there.

 

[bel12345]

Hypotenuse = x+3
1 of Sides = x
Other side = sqrt (6x+9)

Perimiter = 10

2x+(sqrt(6x+9)) = 7

Yes you could use trial and error to find x... but ud have to be pretty lucky

 

[Mark576]

Why would you use trial and error?

2x + sq. rt. (6x + 9) = 7

sq. rt. (6x + 9) = (7 - 2x)

Square both sides;

6x + 9 = 49 - 28x + 4x^2

Use the quadratic formula.

 

[watatank]

and you found the length of the shortest side

add three to get the hypotenuse.

 

[bel12345]

Why would you use trial and error?

2x + sq. rt. (6x + 9) = 7

sq. rt. (6x + 9) = (7 - 2x)

Square both sides;

6x + 9 = 49 - 28x + 4x^2

Use the quadratic formula.

My bad! wont happen agen ey btw are you close 2 narara high?

Answer
Shortest side = 1.410545827
Hypotenuse = 4.410545827
Other side = 4.178908346
Perimiter =10

How to solve it:
Use the quadratic formula in the equation of 0=4x^2 - 34x + 40
Quadratic formula = (-b +- (sqrt(b^2 - 4*a*c)))/2a

 

[Farwa]

the question is wrong, tell your teacher its N/A

 

[Mark576]

My bad! wont happen agen ey btw are you close 2 narara high?

Yeah, Gosford High.

 

[acevipa]

Might seem a bit late now. Though just for reference:

hypotenuse = x+3
shortest side = x

Hence the other side you must work out with pythagoras.

a^2 + b^2 = c^2

Therefore:
(x+3)^2 - x^2 = (Other side)^2
x^2 + 9 - x^2 = (Other side)^2
9 = (Other side)^2
Therefore the other side is equal to the sqrt of 9 which is 3.

So,

hypotenuse = x+3
shortest side = x
other side = 3

Perimeter = (x+3)+x+3
10 = 2x + 6
4=2x
x=2

Therefore hypotenuse is equal to x+3 (2+3)=5cm

 

[Aerath]

Wow Bel. What the hell are you doing in Maths B?

 

[IAU001]

Therefore:
(x+3)^2 - x^2 = (Other side)^2
x^2 + 9 - x^2 = (Other side)^2
9 = (Other side)^2

This is incorrect.
(x+3)^2 - x^2 = (Other side)^2
x^2 + 6x + 9 - x^2 = (Other side)^2 -------------- because (a+b)^2 = a^2 + 2ab + b^2
6x + 9 = (Other side)^2

Excellent attempt though, good job.